AI 中文总结
研究选定可积晶格方程奇点，发现都有三种奇点，包括新的“太势”奇点。详细研究太势与其他奇点相互作用，发现其丰富行为在多方程中存在，且可用控制盒球元胞自动机的符号动力学编码。
AI 中文摘要
我们研究了一些选定的可积晶格方程的奇点，表明它们都具有三种类型的奇点：一种是有限范围的，两种是无限范围的。特别地，我们表明所研究的所有方程都具有一种最近发现的、带状的奇点，即所谓的“太势”。我们详细研究了这些太势与其他两种奇点类型的相互作用，表明在科特韦格 - 德弗里斯方程中首次发现的丰富行为在其他方程中也存在。此外，我们发现所有情况下这种行为都可以用简单的符号动力学来编码，而这正是控制盒球元胞自动机的动力学。
英文摘要
We study the singularities of some selected integrable lattice equations and show they all admit three types of singularities: one of finite and two of infinite extent. In particular, we show that all the equations we study possess a recently discovered, strip-like, singularity which is known under the moniker of ''taishi''. We study in detail the interaction of these taishi with the remaining two types of singularities and show that the rich behaviour first obtained in the case of the Korteweg-deVries equation is also present for other equations. Moreover, we find that in all cases this behaviour can be encoded in terms of simple symbolic dynamics which are just the dynamics governing a Box & Ball cellular automaton.
Comments15 figures; Contribution to the Proceedings of the International Conference on Symmetries and Integrability of Dynamical Systems -- ICSIDS 2024
